Time Allowed: 3 hours Maximum Marks: 80

General Instructions:

1. This Question Paper has 5 Sections A, B, C, D and E.

2. Section A has 20 MCQs carrying 1 mark each

3. Section B has 5 questions carrying 02 marks each.

4. Section C has 6 questions carrying 03 marks each.

5. Section D has 4 questions carrying 05 marks each.

6. Section E has 3 case based integrated units of assessment carrying 04 marks each.

7. All Questions are compulsory. However, an internal choice in 2 Qs of 5 marks, 2 Qs of 3 marks and 2 Questions of
2 marks has been provided. An internal choice has been provided in the 2 marks questions of Section E

8. Draw neat figures wherever required. Take π = wherever required if not stated.
22

Section A
1. The ratio of HCF to LCM of the least composite number and the least prime number is: [1]

a) 1 : 1 b) 2 : 1

c) 1 : 2 d) 1 : 3
2. The graph of y = p(x) is given in the adjoining figure. Zeroes of the polynomial p(x) are [1]

−5
a) −5, 2
,
7

2
,7 b) -5, 7
−5 −7
c) -5, 0, 7 d) 2
,
2

3. The lines represented by the linear equations y = x and x = 4 intersect at P. The coordinates of the point P are: [1]

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 a) (4, 4) b) (-4, 4)

c) (0, 4) d) (4, 0)

4. The length of a rectangular field exceeds its breadth by 8 m and the area of the field is 240 m2. The breadth of [1]

the field is

a) 16 m b) 30 m

c) 12 m d) 20 m
5. The number of terms of an AP 5, 9, 13, …. 185 is: [1]

a) 41 b) 51

c) 31 d) 46
6. The distance between the points (3, -2) and (-3, 2) is: [1]
−−
a) 40 b) 4√10

−− −−
c) 2√10 d) √52

7. x-axis divides the line segment joining A(2, -3) and B(5, 6) in the ratio: [1]

a) 2 : 1 b) 2 : 3

c) 3 : 5 d) 1 : 2
8. In the given figure, AD = 2 cm, DB = 3 cm, DE = 2.5 cm and DE || BC. The value of x is: [1]

a) 7.5 cm b) 3.75 cm

c) 6.25 cm d) 6 cm
9. In the given figure, AB and AC are tangents to the circle with centre O such that ∠BAC = 40°. Then ∠BOC is [1]
equal to

a) 140° b) 120°

c) 80° d) 100°
10. If angle between two radii of a circle is 130 , the angle between tangents at ends of radii is :
o
[1]

a) 70 ∘
b) 90
∘

c) 60 ∘
d) 50
∘

11. sec θ when expressed in terms of cot θ , is equal to: [1]

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 2

a) √1−cot2 θ
b) 1+cot θ

cot θ
cot θ

2
−−−− −−−−
c) √1+cot θ
d) √1 + cot2 θ
cot θ

12. If cos A = , then value of cot A⋅ sin A is: [1]

5

a) 8

5
b) 5

c) d)
8 5

√39 √39

13. The shadow of a 5 m long stick is 2 m long. At the same time, the length of the shadow of a 12.5 m high tree is [1]

a) 3 m b) 4.5 m

c) 3.5 m d) 5 m
14. The area of a sector of angle α (in degrees) of a circle with radius R is: [1]

a) b)
α α 2
× 2πR × πR
180 180

c) α

360
× 2πR d) α

360
× πR
2

15. The area of the sector of a circle of radius 10.5 cm is 69.3 cm2. Find the central angle of the sector. [1]

a) 85o b) 72o

c) 70o d) 26o

16. A die is thrown once. Find the probability of getting a number less than 7. [1]

a) b) 0
1

c) 5

6
d) 1
17. If three coins are tossed simultaneously, what is the probability of getting at most one tail? [1]

a) 3

8
b) 5

c) 7

8
d) 4

18. Mean and median of some data are 32 and 30 respectively. Using empirical relation, mode of the data is: [1]

a) 36 b) 30

c) 20 d) 26
19. Assertion (A): In the given figure, a sphere circumscribes a right cylinder whose height is 8 cm and radius of [1]
the base is 3 cm. The ratio of the surface area of the sphere and the cylinder is 6 : 11

Surface area of sphere

Reason (R): Ratio of their surface area = Surface area of cylinder

a) Both A and R are true and R is the correct b) Both A and R are true but R is not the
explanation of A. correct explanation of A.

c) A is true but R is false. d) A is false but R is true.

20. Assertion (A): The constant difference between any two terms of an AP is commonly known as common [1]
difference.

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 Reason (R): The common difference of 2, 4, 6, 8 this A.P. is 2.

a) Both A and R are true and R is the correct b) Both A and R are true but R is not the
explanation of A. correct explanation of A.

c) A is true but R is false. d) A is false but R is true.

Section B
21. Can two numbers have 15 as their HCF and 175 as their LCM ? Give reasons. [2]
22. State which pairs of triangles in the given figure are similar? Also, state the similarity criterion used. [2]

23. From a point P, 10 cm away from the centre of a circle, a tangent PT of length 8 cm is drawn. Find the radius of [2]
the circle.
24. In △ABC, right-angled at B, AB = 5 cm and ∠ ACB = 30°. Determine the lengths of sides BC and AC. [2]

OR
Prove that (sin θ + cos θ ) (tan θ + cot θ ) = sec θ + cosec θ .
25. A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the minor segment. [Use [2]
π = 3.14.]
OR
Find the area of the minor and the major sectors of a circle with radius 6 cm, if the angle subtended by the minor arc
at the centre is 60o. (Use π = 3.14)
Section C
–
26. Prove that (3 + √2) is irrational. [3]
27. One zero of the polynomial x2- 2x - (7p + 3) is -1, find the value of p and the other zero. [3]

28. Find the value of a, b and c such that the numbers a, 7, b, 23 and c are in A.P. [3]
OR

If the mth term of an A.P. is n

1
and nth term be 1

m
, then show that its (mn)th term is 1.
29. Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the [3]
angle subtended by the line-segment joining the points of contact at the centre.
OR
In the figure, XY and MN are two parallel tangents to a circle with centre O and another tangent AB with point of

contact C intersecting XY at A and MN at B. Prove that ∠ AOB = 90o.

30. If cosec A + cot A = m. show that m −1

2
= cos A. [3]
m +1

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31. Weekly income of 600 families is given below : [3]

Income (in Rs) 0 -1000 1000-2000 2000-3000 3000-4000 4000-5000 5000-6000

No. of Families 250 190 100 40 15 5

Find the median.

Section D
32. A piece of cloth costs 200 Rupees . If the piece was 5 m longer and each metre of cloth costs 2 Rupees less, the [5]
cost of the piece would have remain unchanged. How long is the piece and what is the original rate per metre?
OR
Two pipes together can fill a tank in 15

8
hours. The pipe with larger diameter takes 2 hours less than the pipe with
smaller diameter to fill the tank separately. Find the time in which each pipe can fill the tank separately.
33. From a point P on the ground, the angle of elevation of the top of a 10 m tall building is 30o. A flag is hoisted at [5]

the top of the building and the angle of elevation of the top of the flagstaff from P is 45o. Find the length of the
–
flagstaff and the distance of the building from the point P. (use √3 = 1.73)
34. A wooden article was made by scooping out a hemisphere from each end of a solid cylinder as shown in the [5]
figure. If the height of the cylinder is 10 cm and its base is of radius 3.5 cm, find the total surface area of the
article.

OR
An ice-cream filled cone having radius 5 cm and height 10 cm is as shown in the figure. Find the volume of the ice-
cream in 7 such cones.

35. The following table gives the marks obtained by 50 students in a class test: [5]

Marks 11 - 15 16 - 20 21 - 25 26 - 30 31 - 35 36 - 40 41 - 45 46 - 50

Number of students 2 3 6 7 14 12 4 2

Calculate the mean and median for the above data.

Section E
36. Read the following text carefully and answer the questions that follow: [4]
Architect : An architect is a skilled professional who plans and designs buildings and generally plays a key role
in their construction. Architects are highly trained in the art and science of building design. Since they bear
responsibility for the safety of their buildings’ occupants, architects must be professionally licensed.

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 Vishu is a licensed architect and design very innovative house. She has made a house layout for her client which
is given below. In the layout, the design and measurements has been made such that area of two bedrooms and
kitchen together is 95 sq. m.

i. Which pair of linear equations does describe this situation? (1)

ii. What is the length of the outer boundary of the layout? (1)
iii. What is the area of the bedroom 1? (2)
OR
What is the area of living room in the layout? (2)
37. Read the following text carefully and answer the questions that follow: [4]
Observe the figures given below carefully and answer the questions:
Figure A

Figure B

Figure C

i. Name the figure(s) where in two figures are similar. (1)

ii. Name the figure(s) wherein the figures are congruent. (1)
iii. Prove that congruent triangles are also similar but not the converse. (2)
OR

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 What more is least needed for two similar triangles to be congruent? (2)
38. Read the following text carefully and answer the questions that follow: [4]
A satellite image of a colony is shown below. In this view, a particular house is pointed out by a flag, which is
situated at the point of intersection of x and y-axes. If we go 2 cm east and 3 cm north from the house, then we
reach to a Grocery store. If we go 4 cm west and 6 cm south from the house, then we reach to an Electricians's
shop. If we go 6 cm east and 8 cm south from the house, then we reach to a food cart. If we go 6 cm west and 8
cm north from the house, then we reach a bus stand.
Scale:
x-axis : 1 cm = 1 unit
y-axis : 1 cm = 1 unit

i. What is the distance between the grocery store and food cart? (1)
ii. What is the distance of the bus stand from the house? (1)
iii. If the grocery store and electricians shop lie on a line, then what will be the ratio of distance of house from
grocery store to that from electrician’s shop? (2)
OR
What are the ratio of distances of the house from bus stand to food cart? (2)

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